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A Remark on a Weighted Landau Inequality of Kwong and Zettl

  • R. C. Brown (a1), D. B. Hinton (a2) and M. K. Kwong (a3)

Abstract

In this note we extend a theorem of Kwong and Zettl concerning the inequality

The Kwong-Zettl result holds for 1 ≤ p < ∞ and real numbers α, β, γ such that the conditions (i) β = (α + γ)/2, (ii) β > - 1 , and (iii) γ - 1 - p hold. Here the inequality is proved with β satisfying (i) for all α, γ except p — 1,-1 — p. In this case the inequality is false; however u is shown to satisfy the inequality

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References

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1. Brown, R. C. and Hinton, D. B., Sufficient conditions for weighted inequalities of sum form, J. Math. Anal. Appl. 123(1985), 563578.
2. Brown, R. C., Interpolation inequalities with power weights for functions of one variable, J. Math. Anal. Appl. 172(1993), 233240.
3. Gabushin, V. N., Inequalities for norms of a function and its derivatives in Lp metrics, Mat. Zametki 1(1967), 291298.
4. De Guzman, M., Differentiation of Integrals in 葷n , Lecture Notes in Math. 481, Springer-Verlag, Berlin, 1975.
5. Kwong, M. K. and Zettl, A., Norm inequalities of product form in weighted LP spaces, Proc. Roy. Soc. Edinburgh Sect. A 89(1981), 293307.
6. Opic, B. and Kufner, A., Hardy-type Inequalities, Longman Sci. Tech., Harlow, Essex, United Kingdom, 1990.
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A Remark on a Weighted Landau Inequality of Kwong and Zettl

  • R. C. Brown (a1), D. B. Hinton (a2) and M. K. Kwong (a3)

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